Any cpu that is 333 can run at 266. However, it will run slowly. If you take a 333 Barton that is supposed run with 2.166 ghz (13x166) and put it in a 266 motherboard, it will run at 266x13 = 1.729 ghz, so you lose a lot of speed.
In some cases, with older amd's (nothing that is currently manufactured, but stuff that was manufactured a year or more ago), you can unlock the multiplier, so you can raise the multiplier to compensate for the lower external frequency.
If you have a 266 motherboard, it probably does not have a bios available capable of recognizing a Barton, so you shouldn't buy a barton for it. Best case is it won't recognize the 512 cache and will run it like a 256. Worst case you won't even get the features of thoroughbred or palomino and it will just call it unrecognized cpu. In some cases, you can even lose SSE, it all depends on the bios and motherboard.
That being said, there is no advantage to using a 333 mhz chip, and it will require you physically modding the chip. To unlock mults you have to fill in the pits between the bridges with non conductive goop, then you have to use conductive paint or pencil to connect certain bridges. If you screw it up, you can be out a cpu.
All the new processors cannot be unlocked this way though.